Suitable families of random variables having power series distributions are con-sidered, and their asymptotic behavior in terms of large (and moderate) deviations is studied. Two examples of fractional counting processes are presented, where the normalizations of the involved power series distributions can be expressed in terms of the Prabhakar function. The first example allows to consider the counting process in [Integral Transforms Spec. Funct. 27 (2016), 783-793], the second one is inspired by a model studied in [J. Appl. Probab. 52 (2015), 18-36].

Asymptotic results for families of random variables having power series distributions / C. Macci, B. Pacchiarotti, E. Villa. - In: MODERN STOCHASTICS: THEORY AND APPLICATIONS. - ISSN 2351-6054. - 9:2(2022 May), pp. 207-228. [10.15559/21-VMSTA198]

Asymptotic results for families of random variables having power series distributions

E. Villa
Ultimo
2022

Abstract

Suitable families of random variables having power series distributions are con-sidered, and their asymptotic behavior in terms of large (and moderate) deviations is studied. Two examples of fractional counting processes are presented, where the normalizations of the involved power series distributions can be expressed in terms of the Prabhakar function. The first example allows to consider the counting process in [Integral Transforms Spec. Funct. 27 (2016), 783-793], the second one is inspired by a model studied in [J. Appl. Probab. 52 (2015), 18-36].
Fractional counting processes; large deviations; Mittag-Leffler functions; moderate deviations;
Settore MAT/06 - Probabilita' e Statistica Matematica
mag-2022
3-feb-2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/917906
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